In orbifold gauge theories localized tadpoles can be radiatively generated at the fixed points where U(1) subgroups are conserved. If the Standard Model Higgs fields are identified with internal components of the bulk gauge fields (Higgs-gauge unification) in the presence of these tadpoles the Higgs mass becomes sensitive to the UV cutoff and electroweak symmetry breaking is spoiled. We find the general conditions, based on symmetry arguments, for the absence/presence of localized tadpoles in

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... dels with an arbitrary number of dimensions D. We show that in the class of orbifold compactifications based on T^D-4/Z_N (D even, N>2) tadpoles are always allowed, while on T^D-4/ Z_2 (arbitrary D) with fermions in arbitrary representations of the bulk gauge group tadpoles can only appear in D=6 dimensions. We explicitly check this with one- and two-loops calculations